Optimal current switching control of electrodynamic tethers for fast deorbit

Electrodynamic tethers have the ability to remove space debris from Earth's orbit without the use of propellant. Unfortunately, the periodic variations of electrodynamic force will lead to the tumbling of tethers, and attitude control is needed to achieve a successful deorbit of space debris at the cost of deorbit efficiency. This paper develops an optimal current switching control scheme to enable a fast and stable spacecraft deorbit simultaneously by electrodynamic tethers. In addition, the computational effort of the proposed optimal control is significantly reduced by using a piecewise treatment that discretizes the deorbit process into consecutive time intervals. Within each interval, the system dynamic model is simplified based on different timescales of state variables and the current on-off switching is optimized by solving a constrained minimization problem of a control index representing the deorbit efficiency. Direct Hermite-Simpson discretization is adopted to convert the optimal control problem into a standard nonlinear programming problem. The validity and efficiency of the proposed control strategy is shown by numerical simulations. The deorbit rate increases significantly with the proposed optimal current switching control compared with the existing simple current on-off switch, whereas the computational efforts are reduced.